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The temperature at a point (x, y, z) is given by e-x²-3y²-72² T(x, y, z) = 400e where T is measured in ºC and x, y, z in meters. (a) Find the rate of change of temperature (in "C/m) at the point P(2, -1, 4) in the direction toward the point (3, -3, 6). -29600 x °C/m (b) In which direction does the temperature increase fastest at P? (4,-1,2) x (c) Find the maximum rate of increase at P. 800e -47221 X

The temperature at a point (x, y, z) is given by e-x²-3y²-72² T(x, y, z) = 400e where T is measured in ºC and x, y, z in meters. (a) Find the rate of change of temperature (in "C/m) at the point P(2, -1, 4) in the direction toward the point (3, -3, 6). -29600 x °C/m (b) In which direction does the temperature increase fastest at P? (4,-1,2) x (c) Find the maximum rate of increase at P. 800e -47221 X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The temperature at a point (x, y, z) is given by T(x, y, 2) = 400e-x²-3x²-72² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 4) in the direction toward the point (3, -3, 6). 29600 ¹¹√9 (b) In which direction does the temperature increase fastest at P? (4,-1,2) x X °C/m (c) Find the maximum rate of increase at P. 800e -47 221 x
Transcribed Image Text:The temperature at a point (x, y, z) is given by T(x, y, 2) = 400e-x²-3x²-72² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(2, -1, 4) in the direction toward the point (3, -3, 6). 29600 ¹¹√9 (b) In which direction does the temperature increase fastest at P? (4,-1,2) x X °C/m (c) Find the maximum rate of increase at P. 800e -47 221 x
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